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anonymous
 one year ago
***PLEASE HELP! WILL MEDAL***Express answer in exact form.
Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long
anonymous
 one year ago
***PLEASE HELP! WILL MEDAL***Express answer in exact form. Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When the radius of the circle is 8" and chord length is also 8" Then this chord forms an equilateral triangle a the center . The angle subtended by the chord/arc at the center is also 60° or π/3 radians Area of the larger segment = Area of the circle − area of the smaller segment Area of the smaller segment = Area of the sector − area of the equilateral triangle formed by the chord at the center Area of a sector = ½ R² θ where θ is the angle in radians subtended by the arc at the center of the circle =½×8²×π/3=32π/3 inch ² Area of equilateral triangle of side 8 "=½×8×8sin60° =32×√3/2 =16√3 inch² Hence Area of the smaller segment = 32π/3 − 16√3 Area of the circle =πR²=π×8²=64π inch² Hence area of larger segment =Area of the circle − area of the smaller segment =64π−{32π/3 − 16√3}= 160π/3 + 16√3 inch²

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Give me a sec to read it all

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Or Area = 64pi  (128pi^396root3)/6

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Did you get it right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah that's what I'm thinking

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0didn't really help, but okay

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Two radii and the chord all = 8" All three sides of the triangle so formed are equal. Each of the angles of an equilateral triangle = 60 Degree. Area of a pie piece (called a circle sector) = central angle over entire angle of a circle * r^2 Area of sector = 60/ 360 * pi * r^2 Area of sector = 1/6 * 3.14 * 8^2 Area of sector = 33.51 square inches. Now find the area of an equilateral Triangle. The area of a triangle is the base * height /2 The height = sqr(8^2  4^2) = sqr(48) = 6.928 The area of the triangle = 8*6.928/2 = 27.712 So the area of the smaller segment = area of the sector  area of the triangle small segment = 33.1  27.712 = 5.798 square inches.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's fine. I'm just a little slow that's all. I've never been taught any of this before

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I really can't help it @AnasAlazzawi
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